NORTH LAS VEGAS — Marco Rubio, enmeshed in a heated Republican presidential primary, is sounding more like a candidate pitching himself to a broader general election audience.

Hopscotching across the country Sunday from suburban Nashville to Little Rock to the Las Vegas area, the Florida senator spoke in broad strokes about the racial diversity of his backers, his immigrant family's journey to America and the characteristics that he feels all Americans share.

Rubio, who will barnstorm Nevada on Monday ahead of Tuesday's caucuses, has touched on these themes many times before. But coming out of a strong second-place showing in South Carolina on Saturday, he seems to be emphasizing them more and aiming his message at a broader audience.

"There are a lot of people here today," he said in Franklin, Tenn. "Only a few of you have I ever met in person. I don't know your personal story. And yet I know this: Because you are Americans, you, like me, are just a generation or two removed from someone who made your future the purpose of their lives as well."

Here in a ballroom at a casino hotel Sunday night, Rubio recalled recently being asked about the GOP's minority outreach and responding with a story about the ethnically diverse coalition of South Carolina leaders who backed him.

"I said, well, just this afternoon, I was on stage receiving the endorsement of an Indian American governor from South Carolina, who has endorsed a Cuban American from Florida. And I was standing next to the African American Republican senator from South Carolina. That sounds pretty minority to me."

A central argument in Rubio's attempt to distinguish himself from Sen. Ted Cruz (Tex.) and Donald Trump is his oft-stated belief that he can unite the party more effectively and give Republicans a better chance to win the general election.

"We are the party of everyone. We are going to grow this party and take our message to everyone," Rubio said.

The pace of the primary campaign is beginning to pick up. A week after Tuesday's caucuses, a dozen states will hold nominating contests. Until now the votes have been spaced out and held one at a time so candidates have been able to tailor their messages accordingly.

Rubio is still hitting themes aimed at conservative audiences. For example, he promised Sunday to fight Obamacare and appoint Supreme Court justices who hew to the Constitution's original meaning.

But more and more, he's sounding a unity theme that an already nominated Republican would be expected to emphasize.

"Americans are the descendants of people that came here whether it was two centuries ago or two years ago because they refused to live in a society that told them that they could not be who they wanted to be," Rubio said in Franklin. "America is the descendants of slaves who overcame that horrifying institution to claim their stake to the American dream."